330,904 research outputs found
Analysis of ensemble learning using simple perceptrons based on online learning theory
Ensemble learning of nonlinear perceptrons, which determine their outputs
by sign functions, is discussed within the framework of online learning and
statistical mechanics. One purpose of statistical learning theory is to
theoretically obtain the generalization error. This paper shows that ensemble
generalization error can be calculated by using two order parameters, that is,
the similarity between a teacher and a student, and the similarity among
students. The differential equations that describe the dynamical behaviors of
these order parameters are derived in the case of general learning rules. The
concrete forms of these differential equations are derived analytically in the
cases of three well-known rules: Hebbian learning, perceptron learning and
AdaTron learning. Ensemble generalization errors of these three rules are
calculated by using the results determined by solving their differential
equations. As a result, these three rules show different characteristics in
their affinity for ensemble learning, that is ``maintaining variety among
students." Results show that AdaTron learning is superior to the other two
rules with respect to that affinity.Comment: 30 pages, 17 figure
Good edit similarity learning by loss minimization
International audienceSimilarity functions are a fundamental component of many learning algorithms. When dealing with string or tree-structured data, edit distancebased measures are widely used, and there exists a few methods for learning them from data. However, these methods offer no theoretical guarantee as to the generalization ability and discriminative power of the learned similarities. In this paper, we propose a loss minimization-based edit similarity learning approach, called GESL. It is driven by the notion of (e, γ, τ )-goodness, a theory that bridges the gap between the properties of a similarity function and its performance in classification. We show that our learning framework is a suitable way to deal not only with strings but also with tree-structured data. Using the notion of uniform stability, we derive generalization guarantees for a large class of loss functions. We also provide experimental results on two realworld datasets which show that edit similarities learned with GESL induce more accurate and sparser classifiers than other (standard or learned) edit similarities
Fuzzy ART Choice Functions
Adaptive Resonance Theory (ART) models are real-time neural networks for category learning, pattern recognition, and prediction. Unsupervised fuzzy ART and supervised fuzzy ARTMAP networks synthesize fuzzy logic and ART by exploiting the formal similarity between tile computations of fuzzy subsethood and the dynamics of ART category choice, search, and learning. Fuzzy ART self-organizes stable recognition categories in response to arbitrary sequences of analog or binary input patterns. It generalizes the binary ART 1 model, replacing the set-theoretic intersection (∩) with the fuzzy intersection(∧), or component-wise minimum. A normalization procedure called complement coding leads to a symmetric theory in which the fuzzy intersection and the fuzzy union (∨), or component-wise maximum, play complementary roles. A geometric interpretation of fuzzy ART represents each category as a box that increases in size as weights decrease. This paper analyzes fuzzy ART models that employ various choice functions for category selection. One such function minimizes total weight change during learning. Benchmark simulations compare peformance of fuzzy ARTMAP systems that use different choice functions.Advanced Research Projects Agency (ONR N00014-92-J-4015); National Science Foundation (IRI-90-00530); Office of Naval Research (N00014-91-J-4100
Exact Computation of a Manifold Metric, via Lipschitz Embeddings and Shortest Paths on a Graph
Data-sensitive metrics adapt distances locally based the density of data
points with the goal of aligning distances and some notion of similarity. In
this paper, we give the first exact algorithm for computing a data-sensitive
metric called the nearest neighbor metric. In fact, we prove the surprising
result that a previously published -approximation is an exact algorithm.
The nearest neighbor metric can be viewed as a special case of a
density-based distance used in machine learning, or it can be seen as an
example of a manifold metric. Previous computational research on such metrics
despaired of computing exact distances on account of the apparent difficulty of
minimizing over all continuous paths between a pair of points. We leverage the
exact computation of the nearest neighbor metric to compute sparse spanners and
persistent homology. We also explore the behavior of the metric built from
point sets drawn from an underlying distribution and consider the more general
case of inputs that are finite collections of path-connected compact sets.
The main results connect several classical theories such as the conformal
change of Riemannian metrics, the theory of positive definite functions of
Schoenberg, and screw function theory of Schoenberg and Von Neumann. We develop
novel proof techniques based on the combination of screw functions and
Lipschitz extensions that may be of independent interest.Comment: 15 page
Simple to Complex Cross-modal Learning to Rank
The heterogeneity-gap between different modalities brings a significant
challenge to multimedia information retrieval. Some studies formalize the
cross-modal retrieval tasks as a ranking problem and learn a shared multi-modal
embedding space to measure the cross-modality similarity. However, previous
methods often establish the shared embedding space based on linear mapping
functions which might not be sophisticated enough to reveal more complicated
inter-modal correspondences. Additionally, current studies assume that the
rankings are of equal importance, and thus all rankings are used
simultaneously, or a small number of rankings are selected randomly to train
the embedding space at each iteration. Such strategies, however, always suffer
from outliers as well as reduced generalization capability due to their lack of
insightful understanding of procedure of human cognition. In this paper, we
involve the self-paced learning theory with diversity into the cross-modal
learning to rank and learn an optimal multi-modal embedding space based on
non-linear mapping functions. This strategy enhances the model's robustness to
outliers and achieves better generalization via training the model gradually
from easy rankings by diverse queries to more complex ones. An efficient
alternative algorithm is exploited to solve the proposed challenging problem
with fast convergence in practice. Extensive experimental results on several
benchmark datasets indicate that the proposed method achieves significant
improvements over the state-of-the-arts in this literature.Comment: 14 pages; Accepted by Computer Vision and Image Understandin
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